Problem: Simplify the following expression: $r = \dfrac{-11a - 44}{-55a + 99}$ You can assume $a \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-11a - 44 = - (11 \cdot a) - (2\cdot2\cdot11)$ The denominator can be factored: $-55a + 99 = - (5\cdot11 \cdot a) + (3\cdot3\cdot11)$ The greatest common factor of all the terms is $11$ Factoring out $11$ gives us: $r = \dfrac{(11)(-a - 4)}{(11)(-5a + 9)}$ Dividing both the numerator and denominator by $11$ gives: $r = \dfrac{-a - 4}{-5a + 9}$